Question: Multiply.
$516 \times42$ and $516 \times 4.2$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $516\times 42$. Then we can estimate to place the decimal point in the product of $516 \times 4.2$. $\begin{aligned} 516&\\ \underline{ \times 42}&\\ 12}\\ 20}\\ 1{,}000}\\ 240}\\ 400}\\ \underline{+20{,}000}}\\ 21{,}672 \end{aligned}$ Let's estimate to place the decimal in $516 \times 4.2$. $\begin{aligned} 516 \times 4.2 &\approx 500\times 4\\\\ &\approx 2{,}000 \end{aligned}$ Where can we place the decimal in $21{,}672$ to get a product close to $2{,}000$ ? $2{,}167.2 =516 \times 4.2$